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Mathematics 24 Online
OpenStudy (anonymous):

verify that the equations are identities: 1+cosy/1-cosy = sin^2y/(1-cos^2y)

hero (hero):

Hint: sin^2y = 1 - cos^2y

hero (hero):

I'm going to show you my steps, although, it might not be the way you learned how to do these.

OpenStudy (anonymous):

I worked through it and got 1-cos^2y/1-cos^y

hero (hero):

I don't believe it is an identity according to my math

OpenStudy (anonymous):

this is how I done it 1-cos^2y/(1-cos^2y)(1+cos^2y)= 1-cos^2y/1-cos^2y

hero (hero):

I'm telling you that I don't believe the identity is true

hero (hero):

I can show you my work. It's pretty simple

OpenStudy (anonymous):

How do you decide which side to start on?

hero (hero):

I'll show you what I did

hero (hero):

I knew that sin^2y = 1 - cos^2y so I substituted that in: \(\large\frac{1+cos x}{1-cos x} = \frac{1-cos^2x}{1-cos^2x} \)

hero (hero):

Now look at the right side. It cancels to 1

hero (hero):

So you have \(\large\frac{1 + cos x}{1-cos x} = 1\)

hero (hero):

Now you multiply both sides by 1 - cos x to get 1 + cos x = 1 - cos x

hero (hero):

and now you can see that \(1 + cos x \ne 1 - cos x\)

hero (hero):

so the identity is false

OpenStudy (anonymous):

thanks

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